University of Southern California

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1 Adapive Spaial-Temporal Image Processig Techiques ad Applicaios o Cluer Rejecio i Remoe Sesig Alexader Taraovsy Uiversiy of Souher Califoria Ceer for Applied Mahemaical Scieces Deparme of Mahemaics Suppored i par by Missile Defese Agecy ad Army Research Office

2 How i Wors: Image Esimaio Cluer Removal ad Targe Deecio High qualiy liear ad oliear spaial-emporal filerig of ohomogeeous i space ad osaioary i ime bacgroud suppressio below he level of sesor oise Ipu frame: CR ~ 000 SCR ~ 0.0 LOS jier ampliude ~ 0.5 pix Exracio opimal deecio ad posiio esimaio of low-iesiy movig objecs cars ships aircrafs missiles ec. 008 Alexader Taraovsy Oupu frame ad sigal exracio: CR ~ SCR ~ 0-0 posiio error <0.05 pix

3 Advaced Spaial-Temporal Image Processig Techiques Problem ad Core Techology eed o improve performace of exisig cluer rejecio ad arge racig sysems Key applicaio: deecio ad racig of wea small arges i heavy cluer wih sesors o movig plaforms E.g. for efficie ballisic ad cruise missile defese wih passive space-based ad airbore sesors Exisig Soluios ad Limiaios Prese spaial ad simple differecig cluer rejecio echiques do o allow for cluer suppressio o he sesor oise level which is ecessary for efficie arge deecio/racig Temporal processig ca o be used effecively due o poor image aligme sub-pixel sabilizaio issues Expesive mechaical sabilizers ad elecroic sabilizaio ew idea ad ovel algorihmic implemeaio: use cluer iself for sabilizaio Poeial Beefis Much beer sysem performace ad poeial savigs due o relaxaio for expesive sabilizaio sysems millios of dollars The echology is sofware based ad rus o a PC bu ca also be implemeed io FPGA o mae i real ime wih high frame raes ad large images 04x Alexader Taraovsy 3

4 Srucure of he Sysem Subjec Subjec of of his his al al Cluer Rejecio CLUR ad Image Sabilizaio Sysem wih Auo-selecio ad Adapive Recofigurable Archiecure Deecio ad Tracig Sysem Ba of Spaial-Temporal CLUR ad Sabilizaio Filers Whieed Daa CLUR Auo-uig ad Auo-selecio Deecio ad Trac-Before-Deec Raw Daa Esimaio / Compesaio of Srog Sigals Graphical User Ierface GUI Trac Iiiaio Cofirmaio ad Deleio Tracig Cluer/Targe Simulaor Preview of Resuls Targe Ideificaio / Classificaio 008 Alexader Taraovsy 4

5 Two Differe Scearios of Ieres Quasi-saioary Codiios: Geosaioary Orbi Oly raslaios should be esimaed ad compesaed for sabilizaio There is o o-saioariy due o sesor moio oly due o sesor vibraios o-saioary Codiios: Ay orbi high ellipic low earh aircraf ec. Roaios should be ae io accou: requires 3D sabilizaio echiques osaioariy due o sesor moio ad oher effecs: requires osaioariy predicio olieariy of earh impri Someimes cao suppress cluer o he oise level eve wih all sacrifices: ovel oliear filerig based rac-before-deec algorihms are eeded 008 Alexader Taraovsy 5

6 Cluer Rejecio ad Scee Sabilizaio: The Problem OBSERVATIOS: he sequece of D frames Z ξ I δ r sesor oise b r cluer bacgrou d m S r uow shif due o r m X r r r ij x i... r sigal from he m - h arge wih he i m K m Y y j I S r r m δ r b r δ r ξ r... m jier iesiy m coordiae s of he m - h arge he pixel i he plai image wih coordiae s x j... where - umber of pixels i he frame GOAL: o build a spaial-emporal S-T filer ha rejecs cluer suppresses i o he level of oise ad simulaeously compesae he jier sabilizes he scee MAI STABILIZATIO IDEA: use cluer which is always more iese compared o sesor oise. The higher iesiy of cluer he beer! I m i y j 008 Alexader Taraovsy 6

7 A Class of Parameric Spaial-Temporal CLUR Filers wih Spliig Approximaio Idea: use a parameric approximaio of cluer ad esimae ieraively he parameers i he widow T alog wih frame aligme Time-space spliig approximaio of cluer: b r θ f r where θ uow esimaed slowly chagig i he widow T frames; f M r chose fucios orhogoal basis : Fourier wavelessplies ec. The he esimae of cluer has he followig form: bˆ r δˆ r M θˆ f r δˆ r 008 Alexader Taraovsy 7

8 Spaial-Temporal CLUR Filer: Ieraive Algorihm Iiializaio: may possible efficie schemes Typical Sep : bˆ Jier esimaio. The esimae obaied from he previous sep is compared wih he -h frame ad he MD-esimae of jier is compued as he soluio of he oliear opimizaio problem δˆ r argmi { Z r bˆ r δ} δ r Esimaio of Parameers. Havig obaied he esimaes δˆs from he previous sep compue he MD esimaes of heas for he -h frame from he miimizaio problem mi r θ Z r M s s T θ f r δˆ s r {θˆ } Cluer Esimaio ad Rejecio. Usig he esimaes of heas ad delas compue he esimae of cluer ad he residuals ~ Z r Z r M θˆ f r δˆ r 008 Alexader Taraovsy 8

9 Developed CLUR Algorihms for SBIRS HIGH geosaioary Spaial-oly i-frame algorihms Spa Temporal filerig i a slidig widow Temp Adapive spaial-emporal auo-regressio STAR Two-dimesioal Fourier series wih double yquis rae Four Two-dimesioal Wavele series Wavele Splie-based Filers Adapive regressio wih bi-liear double-resoluio ierpolaio DRBil : Cubic splie ierpolaio wih double-resoluio DRspl : Local polyomial approximaio Pol 008 Alexader Taraovsy 9

10 008 Alexader Taraovsy 0 Spaial-Temporal Auoregressive STAR Filer Wih Compesaio STAR filer uses rasformed daa wih sigal compesaio form he recagular spaial widow ad emporal widow The vecor of coefficies is compued o miimize he empirical variace of he filer oupu: The compuaios are reduced o solvig he equaio wih he sample covariace: ˆ ˆ T l l l j i Z a T j i b ˆ arg mi j i T l l l j i Z c T j i Z c a ˆ ˆ l j i m Z j r i Z s R T s s s j i y x l m r T s R a R a l a

11 Evaluaio of he Algorihm Qualiy: Performace Idices To compare cluer suppressio algorihms we use he followig simple idices: G-facor: From he poi of view of cluer rejecio a good cluer suppressio algorihm should miimize he value of G σ σ ou / σ ; variace of he sesor oise; σ variace of he oupu frame Q-facor: More impora is he evaluaio of he relaive value of he effecive sigal-clueroise-raio SCR which is equal o i he ideal case cluer compleely suppressed ad here is o sigal degradaio: S i j S ~ / [ i j] / σ ou ij Q SR eff / SR ideal / S i j / σ Jier esimaio MSE: Errors of jier esimaio have a subsaial impac o he performace of cluer suppressio algorihms ad esimaio of arge coordiaes ou ij 008 Alexader Taraovsy

12 Image Characerisics ad Modelig Codiios Simples characerisics which i realisic codiios due o o- Gaussia cluer disribuio are o exhausive iclude: Variace σ b Spaial correlaio coefficie ad he correspodig effecive radius of spaial correlaio Δ0 / ρ Three subsaially differe scearios have bee cosidered: ρ Sceario : Relaively wea cluer wih relaively high spaial variaio σ / σ 5 6; ρ 0.85 b Sceario : Moderaely iese cluer wih very high spaial variaio small correlaio σ / σ 6; ρ 0. b Sceario 3: Relaively iese heavy cluer wih high spaial correlaio σ b / σ 78; ρ Alexader Taraovsy

13 Evaluaio of he Algorihm Qualiy: Simulaio Resuls Sceario : Moderae cluer wih very high spaial variaio: CR.8; ρ 0.; T 0T ; A A G-values mem 0 x y Δ 0 o Filerig Spa Temp STAR Wavele DRspl Pol ! Q-values The bes algorihm Targe Velociy o Filerig Spa Temp STAR Wavele DRspl 0. p/f ! 0.0! p/f ! 0.03! Alexader Taraovsy 3

14 Evaluaio of he Algorihm Qualiy: Simulaio Resuls MSE of jier esimaio i uis of he pixel size Sceario : Sceario : Sceario 3: CR CR CR y 5.4; ρ 0.85; A x A 0.4Δ y 5.8; ρ 0.; A x A 0.4Δ y 78.4; ρ 0.95; A x A 0.4Δ Wavele DRspl DRbil Pol Sceario Sceario Sceario The bes algorihm 008 Alexader Taraovsy 4

15 Resuls of Experimes: Two wea arges Movies SR5 CR50 arge velociy0.5pix jier0.5pix #arges Origial Spaial-oly Spaial-emporal Clic o Play Movies Residual jier is a small fracio of a pixel usually less ha 0% ad ofe -%! 008 Alexader Taraovsy 5

16 Compariso of a Simple Differecig Mehod Wih Our Mehods: Resuls for he Differecig Algorihm Clic o Play Movie 008 Alexader Taraovsy 6

17 Compariso of a Simple Differecig Mehod Wih Our Mehods: Resuls for he STAR Filer Auomaic Selecio STAR Filer Clic o Play Movie 008 Alexader Taraovsy 7

18 osaioary Codiios: Low-Earh Orbi ad High-Earh Ellipic Orbi Saellies While his approach is very effecive for quasi-saioary codiios e.g. geosaioary sarig sesors i does o seem compleely ameable o oher scearios lie low-earh high-ellipic orbis ad aricrafs Therefore a impora direcio of he wor is o modify described image processig echiques ad develop ew mehods ha will be efficie for more difficul o-saioary eviromes characerisic of low-earh orbisec. The cluer rejecio mehod for osaioary codiios i quesio requires o oly raslaioal ad roaioal sabilizaio bu also a sophisicaed image predicio algorihm 008 Alexader Taraovsy 8

19 Specific Feaures o-lieariy of images Sphericiy of he earh should be ae io accou osaioariy relaed o sesor moio Frame shifs i he FOV field of view may be o he order of dozes of pixels which affecs he cluer rejecio ad sabilizaio algorihms. As a resul a wo-sage sabilizaio procedure is eeded» A he firs sage we propose o use a sabilizaio sysem ha allows for ulrahigh speed image sabilizaio roaios ad raslaios reducig jier o he pixel or sub-pixel level» A he secod sage a ieraive supersabilizaio algorihm developed for geosaioary sesors is used o compesae for he remaiig isabiliy 008 Alexader Taraovsy 9

20 Specific Feaures Co. The ecessiy o ideify a 3D cloud cover model For efficie cluer rejecio i is ecessary o accou for a 3D cloud model aliude relief shape of clouds. Complexiy of images ad high cluer-o-oise raio CR For low-orbi sesors oe should ae io cosideraio high CR ad high sigal-o-oise raio SR Complex iesiy disribuio across frames due o discoiuiies of he iesiy fucio o borders of ohomogeous regios o he earh surface I order o suppress such cluer o he level of sesor oise ew cluer rejecio algorihms mus be developed Moderae CR High CR 008 Alexader Taraovsy 0

21 A ovel Robus Mehod The mai feaures of he ovel approach for image esimaio are ha we accou for: Bacgroud dyamics due o wid urbulece ad covecio Dyamics of observaio codiios relaed o he moio of observer ha causes oliear disurbaces ad warpig of cluered bacgrouds ha cao be described by smooh sigle-valued fucios The mai ovely is predicio of image iesiy ha chages due o sesor moio Iesiy deformaios/warpig have a quie complex form ad have o be described by a discoiuous fucio To his ed ew mahemaical echiques are eeded; hese are much more complex ha i he case of he saioary sesor 008 Alexader Taraovsy

22 3-axis Sabilizaio Clic o Play Movie 008 Alexader Taraovsy

23 Cluer Rejecio Resuls: MeeoSa Daa Parameers: Perigee aliude 500m; Apogee aliude 35800m; pix size 35*0^-4 rad; Ipu frame 5x5; Oupu frame 8x8; Frame rae fps CLUR algorihm: Sabilizaio: roaioal shifs scalig CLUR filer: Image predicio based o a parameric model Ipu ad oupu frames parameers: Ipu variace 500; Oupu variace 5; G00 Clic o Play Movie 008 Alexader Taraovsy 3

24 Beefis/Capabiliies We aicipae ha he developed prooype ca be effecively used for he desig ad opimizaio of he real sysem i a variey of codiios meeorological/illumiaio ad sesor/plaform geomeries. I paricular as was discussed above: The algorihms of daa processig esure almos opimum performace of arge deecio posiio esimaio ad racig for he mos difficul cluer scearios i he presece of LOS jier The excelle qualiy of daa processig is achieved due o adapive selecio of he bes for he curre bacgroud algorihm of cluer suppressio amog a se of developed algorihms The algorihms are capable o operae simulaeously wih boh low iesiy sigals SCR abou 0.0 ad high iesiy sigals ad ouliers which should be compesaed o opimize he performace The sofware imbedded io a ierface wih visualizaio cosiue powerful ools for he desig ad opimizaio of he specific sysem i specific codiios of ieres 008 Alexader Taraovsy 4